What is the solution for (dy)/(dx)=-2y+x,y(0)=0 ?

The solution for (dy)/(dx)=-2y+x,y(0)=0 is y=(2x-1)/4+1/(4e^{2x)}

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(dy)/(dx)=-2y+x,y(0)=0

\frac{d y}{d x} = - 2 y + x, y (0) = 0

y = \frac{2 x - 1}{4} + \frac{1}{4 e ^{2 x}}

Solution steps

\frac{d y}{d x} = - 2 y + x

Solve linear ODE:

y = \frac{2 x - 1}{4} + \frac{1}{4 e ^{2 x}}

y = \frac{2 x - 1}{4} + \frac{1}{4 e ^{2 x}}

\frac{d}{d x} (x + x^{2})

\int t^{5} d t

\frac{1}{s ( s + 4 ) ^{2}}

\frac{d}{d x} ((3 x^{2} + 5)^{3} (3 x - 1)^{2})

\int (1 + x^{2})^{- 1} d x

What is the solution for (dy)/(dx)=-2y+x,y(0)=0 ?
The solution for (dy)/(dx)=-2y+x,y(0)=0 is y=(2x-1)/4+1/(4e^{2x)}